by Cáceres and Selling7
who showed that similar behavior
existed irrespective of the type of defect or numbers of de- fects, whether it was porosity, dross, oxides or artificially introduced holes. Bulk volumetric porosity had almost no correlation to tensile properties, whereas the number or proportion of defects present on the fracture surface was directly related to the tensile behavior. Cáceres and Sell- ing7
sectional area containing a defect, Ai
fect, and σh defect.
σi(1-f)Ao Where σi
e-εi =σh Ao and εi e-εh and εh
where f is the area fraction covered by the defect. In this case, load equilibrium is maintained if:
, such that Ai
, and the cross =Ao
Equation 12
are the true stress and strain inside the de- are the true stress and strain outside the
If the material follows the well-known relationship (Lud- wik-Holloman equation): σ = Kεn
(1-f),
elongation, or the true strain at the onset of necking. This means that a defect-free casting will continue to elongate un- til the maximum stress is achieved and necking begins, lead- ing to failure. The presence of defects in the material means that void growth and crack propagation occurs at levels of strength and ductility where ε < n, these levels being pro- portionate to the fraction of defects present in the material.
proposed a model based on the relationship between a cross sectional area not containing a defect, Ao
As an alternate to use of the Ludwik-Holloman equation, the Kocks-Mecking Model and the derivation of the latter to give the Voce equation are based on a first principles ap- proach to strain hardening, and represent an excellent al- ternative.11
Whereas, the Ludwik-Holloman equation may
underestimate experimental results, the Kocks-Mecking Model may have the opposite effect and be less relevant to low levels of strain.11
As may be appreciated, scatter exists
in nominally equivalent material, which suggests that indi- ces based on both models represent the data reasonably well in application.
Equation 13
Where σ is true stress, ε is true plastic strain, K is a constant, known as the strength coefficient and n is the strain harden- ing exponent;
then combining Eqns 12 and 13 leads to: (1-f)e-εi
εi n = e-εh εh n Equation 14
This equation relates the strain inside the defect to the strain outside the defect. As may be appreciated, when solving Eqn 14, as the defect area present on the fracture surface f, increases, for a fixed value of strain outside the defect (εh the strain inside the defect containing region (εi
), ) increases more rapidly.
Quality index for Al castings Quality index (Q) was originally derived by Drouzy et al.8
to
describe the presence, or absence, of casting defects in per- manent mold and sand cast Al-Si-Mg alloys such as A356 and A357. It was first developed as an empirical formula:
Q = UTS+150logEf Where Q and UTS are in MPa and Ef Equation 15 is the percent elonga-
tion at fracture (i.e., elastic + plastic strain). Later, Cáce- res9,10
showed that for any aluminium alloy, derivation of
the flow curve described by the Ludwik-Holloman equation (Eqn 13) could provide the basis for the assignment of qual- ity indices based on proportions of what would constitute a defect-free casting, where the true strain ε = n. Although the Ludwik-Holloman equation is an empirical relationship, n can be shown experimentally to be equivalent to the uniform
International Journal of Metalcasting/Summer 2011
One limitation to the use of the quality index is the fact that, in practice, it is often only used with a small amount of experimental data, or used with average (mean) results obtained from a similarly small number of samples. The combination of these two factors may invalidate conclusions regarding component quality, since the scatter in tensile data is directly related to the flaw size distribution and hence the quality of the cast material. Although average values of elongation and tensile strength are often presented in litera- ture, what are clearly of great importance are the lowest val- ues of mechanical properties as these provide the limits for safe component operation. These lower limits are important because it is these values around which components will (or should) actually be designed.
Experimental methods
HPDC alloy specimens for tensile testing were produced us- ing a Toshiba cold chamber die-casting machine with a 250 ton locking force, a shot sleeve with an internal diameter of 50 mm and a stroke of 280 mm. The die provided two cylin- drical tensile specimens and one flat tensile specimen from each shot, and these all conformed to specification AS1391. The cylindrical tensile test bars used for the current tensile tests had a total length of 100 mm with a central parallel gauge section 33 mm long and a diameter of 5.55 ±0.1 mm. The flat tensile specimen on the runner was not used in the current testing. The first 10 shots in each run were discarded. At least 100 tensile samples (50 shots) were then cast in each batch, from which samples for tensile testing were randomly selected. Tensile testing was conducted following standard procedures, at a strain rate of 5 mm/min.
Degassing was done with a Reading Foundry Products Mod- el RE 2/4 rotary degassing unit, operating at 300 RPM with a flow rate of high purity argon of 7L/minute for 20 minutes (The furnace held approximately 140kg of metal). Reduced
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